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TRS Standard pair #487073319
details
property
value
status
complete
benchmark
023.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n189.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0468451 seconds
cpu usage
0.036581
user time
0.024819
system time
0.011762
max virtual memory
113188.0
max residence set size
5388.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(id,x:S) -> x:S app(plus,0) -> id ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(id,x:S) -> x:S app(plus,0) -> id -> 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(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) APP(app(plus,app(s,x:S)),y:S) -> APP(plus,x:S) APP(app(plus,app(s,x:S)),y:S) -> APP(s,app(app(plus,x:S),y:S)) -> Rules: app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(id,x:S) -> x:S app(plus,0) -> id Problem 1: SCC Processor: -> Pairs: APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) APP(app(plus,app(s,x:S)),y:S) -> APP(plus,x:S) APP(app(plus,app(s,x:S)),y:S) -> APP(s,app(app(plus,x:S),y:S)) -> Rules: app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(id,x:S) -> x:S app(plus,0) -> id ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) ->->-> Rules: app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(id,x:S) -> x:S app(plus,0) -> id Problem 1: Reduction Pairs Processor: -> Pairs: APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) -> Rules: app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(id,x:S) -> x:S app(plus,0) -> id -> Usable rules: app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(id,x:S) -> x:S app(plus,0) -> id ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [app](X1,X2) = X1 + X2 + 2 [0] = 0 [fSNonEmpty] = 0 [id] = 0 [plus] = 1 [s] = 2 [APP](X1,X2) = X1 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(id,x:S) -> x:S app(plus,0) -> id ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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