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TRS Inner 89993 pair #381733530
details
property
value
status
complete
benchmark
#4.20a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.033921957016 seconds
cpu usage
0.026299206
max memory
2945024.0
stage attributes
key
value
output-size
1946
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 x) (RULES f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0)) -> g(f(s(0))) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: F(s(x)) -> F(x) G(s(0)) -> F(s(0)) G(s(0)) -> G(f(s(0))) -> Rules: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0)) -> g(f(s(0))) Problem 1: SCC Processor: -> Pairs: F(s(x)) -> F(x) G(s(0)) -> F(s(0)) G(s(0)) -> G(f(s(0))) -> Rules: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0)) -> g(f(s(0))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x)) -> F(x) ->->-> Rules: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0)) -> g(f(s(0))) ->->Cycle: ->->-> Pairs: G(s(0)) -> G(f(s(0))) ->->-> Rules: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0)) -> g(f(s(0))) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: F(s(x)) -> F(x) -> Rules: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0)) -> g(f(s(0))) ->Projection: pi(F) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0)) -> g(f(s(0))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pairs Processor: -> Pairs: G(s(0)) -> G(f(s(0))) -> Rules: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0)) -> g(f(s(0))) -> Usable rules: f(f(x)) -> f(x) f(s(x)) -> f(x) ->Interpretation type: Linear
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