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TRS Standard pair #516967246
details
property
value
status
complete
benchmark
#3.12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.1391518116 seconds
cpu usage
0.043494623
max memory
3608576.0
stage attributes
key
value
output-size
5561
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 n:S x:S y:S) (RULES app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S reverse(add(n:S,x:S)) -> app(reverse(x:S),add(n:S,nil)) reverse(nil) -> nil shuffle(add(n:S,x:S)) -> add(n:S,shuffle(reverse(x:S))) shuffle(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S reverse(add(n:S,x:S)) -> app(reverse(x:S),add(n:S,nil)) reverse(nil) -> nil shuffle(add(n:S,x:S)) -> add(n:S,shuffle(reverse(x:S))) shuffle(nil) -> nil -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: APP(add(n:S,x:S),y:S) -> APP(x:S,y:S) REVERSE(add(n:S,x:S)) -> APP(reverse(x:S),add(n:S,nil)) REVERSE(add(n:S,x:S)) -> REVERSE(x:S) SHUFFLE(add(n:S,x:S)) -> REVERSE(x:S) SHUFFLE(add(n:S,x:S)) -> SHUFFLE(reverse(x:S)) -> Rules: app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S reverse(add(n:S,x:S)) -> app(reverse(x:S),add(n:S,nil)) reverse(nil) -> nil shuffle(add(n:S,x:S)) -> add(n:S,shuffle(reverse(x:S))) shuffle(nil) -> nil Problem 1: SCC Processor: -> Pairs: APP(add(n:S,x:S),y:S) -> APP(x:S,y:S) REVERSE(add(n:S,x:S)) -> APP(reverse(x:S),add(n:S,nil)) REVERSE(add(n:S,x:S)) -> REVERSE(x:S) SHUFFLE(add(n:S,x:S)) -> REVERSE(x:S) SHUFFLE(add(n:S,x:S)) -> SHUFFLE(reverse(x:S)) -> Rules: app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S reverse(add(n:S,x:S)) -> app(reverse(x:S),add(n:S,nil)) reverse(nil) -> nil shuffle(add(n:S,x:S)) -> add(n:S,shuffle(reverse(x:S))) shuffle(nil) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(add(n:S,x:S),y:S) -> APP(x:S,y:S) ->->-> Rules: app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S reverse(add(n:S,x:S)) -> app(reverse(x:S),add(n:S,nil)) reverse(nil) -> nil shuffle(add(n:S,x:S)) -> add(n:S,shuffle(reverse(x:S))) shuffle(nil) -> nil ->->Cycle: ->->-> Pairs: REVERSE(add(n:S,x:S)) -> REVERSE(x:S) ->->-> Rules: app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S reverse(add(n:S,x:S)) -> app(reverse(x:S),add(n:S,nil)) reverse(nil) -> nil shuffle(add(n:S,x:S)) -> add(n:S,shuffle(reverse(x:S))) shuffle(nil) -> nil ->->Cycle: ->->-> Pairs: SHUFFLE(add(n:S,x:S)) -> SHUFFLE(reverse(x:S)) ->->-> Rules: app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S reverse(add(n:S,x:S)) -> app(reverse(x:S),add(n:S,nil)) reverse(nil) -> nil shuffle(add(n:S,x:S)) -> add(n:S,shuffle(reverse(x:S))) shuffle(nil) -> nil The problem is decomposed in 3 subproblems.
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