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TRS Standard pair #487073594
details
property
value
status
complete
benchmark
BTreeMember.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
Applicative_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.026366 seconds
cpu usage
0.026847
user time
0.012418
system time
0.014429
max virtual memory
113188.0
max residence set size
5660.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S w:S x:S y:S z:S) (RULES app(app(eq,app(s,x:S)),0) -> ffalse app(app(eq,0),app(s,x:S)) -> ffalse app(app(eq,x:S),x:S) -> ttrue app(app(lt,app(s,x:S)),app(s,y:S)) -> app(app(lt,x:S),y:S) app(app(lt,0),app(s,y:S)) -> ttrue app(app(lt,y:S),0) -> ffalse app(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> app(app(app(if,app(app(lt,w:S),y:S)),app(app(member,w:S),x:S)),app(app(app(if,app(app(eq,w:S),y:S)),ttrue),app(app(member,w:S),z:S))) app(app(member,w:S),null) -> ffalse ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(eq,app(s,x:S)),0) -> ffalse app(app(eq,0),app(s,x:S)) -> ffalse app(app(eq,x:S),x:S) -> ttrue app(app(lt,app(s,x:S)),app(s,y:S)) -> app(app(lt,x:S),y:S) app(app(lt,0),app(s,y:S)) -> ttrue app(app(lt,y:S),0) -> ffalse app(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> app(app(app(if,app(app(lt,w:S),y:S)),app(app(member,w:S),x:S)),app(app(app(if,app(app(eq,w:S),y:S)),ttrue),app(app(member,w:S),z:S))) app(app(member,w:S),null) -> ffalse -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: APP(app(lt,app(s,x:S)),app(s,y:S)) -> APP(app(lt,x:S),y:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(app(if,app(app(eq,w:S),y:S)),ttrue),app(app(member,w:S),z:S)) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(app(if,app(app(lt,w:S),y:S)),app(app(member,w:S),x:S)),app(app(app(if,app(app(eq,w:S),y:S)),ttrue),app(app(member,w:S),z:S))) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(eq,w:S),y:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(if,app(app(eq,w:S),y:S)),ttrue) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(if,app(app(lt,w:S),y:S)),app(app(member,w:S),x:S)) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(lt,w:S),y:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(member,w:S),x:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(member,w:S),z:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(if,app(app(eq,w:S),y:S)) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(if,app(app(lt,w:S),y:S)) -> Rules: app(app(eq,app(s,x:S)),0) -> ffalse app(app(eq,0),app(s,x:S)) -> ffalse app(app(eq,x:S),x:S) -> ttrue app(app(lt,app(s,x:S)),app(s,y:S)) -> app(app(lt,x:S),y:S) app(app(lt,0),app(s,y:S)) -> ttrue app(app(lt,y:S),0) -> ffalse app(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> app(app(app(if,app(app(lt,w:S),y:S)),app(app(member,w:S),x:S)),app(app(app(if,app(app(eq,w:S),y:S)),ttrue),app(app(member,w:S),z:S))) app(app(member,w:S),null) -> ffalse Problem 1: SCC Processor: -> Pairs: APP(app(lt,app(s,x:S)),app(s,y:S)) -> APP(app(lt,x:S),y:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(app(if,app(app(eq,w:S),y:S)),ttrue),app(app(member,w:S),z:S)) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(app(if,app(app(lt,w:S),y:S)),app(app(member,w:S),x:S)),app(app(app(if,app(app(eq,w:S),y:S)),ttrue),app(app(member,w:S),z:S))) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(eq,w:S),y:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(if,app(app(eq,w:S),y:S)),ttrue) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(if,app(app(lt,w:S),y:S)),app(app(member,w:S),x:S)) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(lt,w:S),y:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(member,w:S),x:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(member,w:S),z:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(if,app(app(eq,w:S),y:S)) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(if,app(app(lt,w:S),y:S)) -> Rules: app(app(eq,app(s,x:S)),0) -> ffalse app(app(eq,0),app(s,x:S)) -> ffalse app(app(eq,x:S),x:S) -> ttrue app(app(lt,app(s,x:S)),app(s,y:S)) -> app(app(lt,x:S),y:S) app(app(lt,0),app(s,y:S)) -> ttrue app(app(lt,y:S),0) -> ffalse app(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> app(app(app(if,app(app(lt,w:S),y:S)),app(app(member,w:S),x:S)),app(app(app(if,app(app(eq,w:S),y:S)),ttrue),app(app(member,w:S),z:S))) app(app(member,w:S),null) -> ffalse ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(lt,app(s,x:S)),app(s,y:S)) -> APP(app(lt,x:S),y:S) ->->-> Rules: app(app(eq,app(s,x:S)),0) -> ffalse app(app(eq,0),app(s,x:S)) -> ffalse app(app(eq,x:S),x:S) -> ttrue app(app(lt,app(s,x:S)),app(s,y:S)) -> app(app(lt,x:S),y:S) app(app(lt,0),app(s,y:S)) -> ttrue app(app(lt,y:S),0) -> ffalse app(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> app(app(app(if,app(app(lt,w:S),y:S)),app(app(member,w:S),x:S)),app(app(app(if,app(app(eq,w:S),y:S)),ttrue),app(app(member,w:S),z:S))) app(app(member,w:S),null) -> ffalse ->->Cycle: ->->-> Pairs: APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(member,w:S),x:S) APP(app(member,w:S),app(app(app(fork,x:S),y:S),z:S)) -> APP(app(member,w:S),z:S) ->->-> Rules: app(app(eq,app(s,x:S)),0) -> ffalse app(app(eq,0),app(s,x:S)) -> ffalse
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