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TRS Standard pair #516964906
details
property
value
status
complete
benchmark
08.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Applicative_first_order_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.107603788376 seconds
cpu usage
0.045807385
max memory
2809856.0
stage attributes
key
value
output-size
13231
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 f:S x:S xs:S y:S) (RULES app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S) app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S)) app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S) app(app(filter,f:S),nil) -> nil app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(D,app(app(*,x:S),y:S)) -> app(app(+,app(app(*,y:S),app(D,x:S))),app(app(*,x:S),app(D,y:S))) app(D,app(app(+,x:S),y:S)) -> app(app(+,app(D,x:S)),app(D,y:S)) app(D,app(app(-,x:S),y:S)) -> app(app(-,app(D,x:S)),app(D,y:S)) app(D,constant) -> 0 app(D,t) -> 1 ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S) app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S)) app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S) app(app(filter,f:S),nil) -> nil app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(D,app(app(*,x:S),y:S)) -> app(app(+,app(app(*,y:S),app(D,x:S))),app(app(*,x:S),app(D,y:S))) app(D,app(app(+,x:S),y:S)) -> app(app(+,app(D,x:S)),app(D,y:S)) app(D,app(app(-,x:S),y:S)) -> app(app(-,app(D,x:S)),app(D,y:S)) app(D,constant) -> 0 app(D,t) -> 1 -> 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(app(app(filter2,ffalse),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S) APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(cons,x:S),app(app(filter,f:S),xs:S)) APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(filter2,app(f:S,x:S)),f:S),x:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(filter2,app(f:S,x:S)),f:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(filter2,app(f:S,x:S)) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(f:S,x:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) APP(D,app(app(*,x:S),y:S)) -> APP(app(*,x:S),app(D,y:S)) APP(D,app(app(*,x:S),y:S)) -> APP(app(*,y:S),app(D,x:S)) APP(D,app(app(*,x:S),y:S)) -> APP(app(+,app(app(*,y:S),app(D,x:S))),app(app(*,x:S),app(D,y:S))) APP(D,app(app(*,x:S),y:S)) -> APP(+,app(app(*,y:S),app(D,x:S))) APP(D,app(app(*,x:S),y:S)) -> APP(D,x:S) APP(D,app(app(*,x:S),y:S)) -> APP(D,y:S) APP(D,app(app(+,x:S),y:S)) -> APP(app(+,app(D,x:S)),app(D,y:S)) APP(D,app(app(+,x:S),y:S)) -> APP(+,app(D,x:S)) APP(D,app(app(+,x:S),y:S)) -> APP(D,x:S) APP(D,app(app(+,x:S),y:S)) -> APP(D,y:S) APP(D,app(app(-,x:S),y:S)) -> APP(app(-,app(D,x:S)),app(D,y:S)) APP(D,app(app(-,x:S),y:S)) -> APP(-,app(D,x:S)) APP(D,app(app(-,x:S),y:S)) -> APP(D,x:S) APP(D,app(app(-,x:S),y:S)) -> APP(D,y:S) -> Rules: app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S) app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S)) app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S) app(app(filter,f:S),nil) -> nil app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(D,app(app(*,x:S),y:S)) -> app(app(+,app(app(*,y:S),app(D,x:S))),app(app(*,x:S),app(D,y:S))) app(D,app(app(+,x:S),y:S)) -> app(app(+,app(D,x:S)),app(D,y:S)) app(D,app(app(-,x:S),y:S)) -> app(app(-,app(D,x:S)),app(D,y:S)) app(D,constant) -> 0 app(D,t) -> 1 Problem 1: SCC Processor: -> Pairs: APP(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S) APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(cons,x:S),app(app(filter,f:S),xs:S)) APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(filter2,app(f:S,x:S)),f:S),x:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(filter2,app(f:S,x:S)),f:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(filter2,app(f:S,x:S)) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S)
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