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TRS Stand 20472 pair #381712958
details
property
value
status
complete
benchmark
22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n024.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0494141578674 seconds
cpu usage
0.029187282
max memory
3059712.0
stage attributes
key
value
output-size
2305
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 y) (RULES f(s(x),s(y)) -> s(f(x,y)) f(x,0) -> s(0) g(0,x) -> g(f(x,x),x) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(s(x),s(y)) -> s(f(x,y)) f(x,0) -> s(0) g(0,x) -> g(f(x,x),x) -> 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)) -> F(x,y) G(0,x) -> F(x,x) G(0,x) -> G(f(x,x),x) -> Rules: f(s(x),s(y)) -> s(f(x,y)) f(x,0) -> s(0) g(0,x) -> g(f(x,x),x) Problem 1: SCC Processor: -> Pairs: F(s(x),s(y)) -> F(x,y) G(0,x) -> F(x,x) G(0,x) -> G(f(x,x),x) -> Rules: f(s(x),s(y)) -> s(f(x,y)) f(x,0) -> s(0) g(0,x) -> g(f(x,x),x) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x),s(y)) -> F(x,y) ->->-> Rules: f(s(x),s(y)) -> s(f(x,y)) f(x,0) -> s(0) g(0,x) -> g(f(x,x),x) ->->Cycle: ->->-> Pairs: G(0,x) -> G(f(x,x),x) ->->-> Rules: f(s(x),s(y)) -> s(f(x,y)) f(x,0) -> s(0) g(0,x) -> g(f(x,x),x) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: F(s(x),s(y)) -> F(x,y) -> Rules: f(s(x),s(y)) -> s(f(x,y)) f(x,0) -> s(0) g(0,x) -> g(f(x,x),x) ->Projection: pi(F) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: f(s(x),s(y)) -> s(f(x,y)) f(x,0) -> s(0) g(0,x) -> g(f(x,x),x) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pairs Processor: -> Pairs: G(0,x) -> G(f(x,x),x)
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