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TRS Standard pair #516967401
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
n094.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0302920341492 seconds
cpu usage
0.026447406
max memory
2068480.0
stage attributes
key
value
output-size
8439
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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:
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