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TRS Standard pair #516967061
details
property
value
status
complete
benchmark
#3.23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n115.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.079715013504 seconds
cpu usage
0.037979575
max memory
3149824.0
stage attributes
key
value
output-size
2203
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES f(0,y:S) -> 0 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(0,y:S) -> 0 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: F(s(x:S),y:S) -> F(f(x:S,y:S),y:S) F(s(x:S),y:S) -> F(x:S,y:S) -> Rules: f(0,y:S) -> 0 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S) Problem 1: SCC Processor: -> Pairs: F(s(x:S),y:S) -> F(f(x:S,y:S),y:S) F(s(x:S),y:S) -> F(x:S,y:S) -> Rules: f(0,y:S) -> 0 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x:S),y:S) -> F(f(x:S,y:S),y:S) F(s(x:S),y:S) -> F(x:S,y:S) ->->-> Rules: f(0,y:S) -> 0 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S) Problem 1: Reduction Pairs Processor: -> Pairs: F(s(x:S),y:S) -> F(f(x:S,y:S),y:S) F(s(x:S),y:S) -> F(x:S,y:S) -> Rules: f(0,y:S) -> 0 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S) -> Usable rules: f(0,y:S) -> 0 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = 2.X1 [0] = 2 [fSNonEmpty] = 0 [s](X) = 2.X + 2 [F](X1,X2) = 2.X1 Problem 1: SCC Processor: -> Pairs: F(s(x:S),y:S) -> F(x:S,y:S) -> Rules: f(0,y:S) -> 0 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x:S),y:S) -> F(x:S,y:S) ->->-> Rules: f(0,y:S) -> 0 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S) Problem 1: Subterm Processor:
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