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TRS Standard pair #516966876
details
property
value
status
complete
benchmark
2.41.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n120.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0719408988953 seconds
cpu usage
0.020124351
max memory
1871872.0
stage attributes
key
value
output-size
4655
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 x:S y:S z:S) (RULES f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: F(x:S,g(y:S,z:S)) -> F(x:S,y:S) NORM(g(x:S,y:S)) -> NORM(x:S) REM(g(x:S,y:S),s(z:S)) -> REM(x:S,z:S) -> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil Problem 1: SCC Processor: -> Pairs: F(x:S,g(y:S,z:S)) -> F(x:S,y:S) NORM(g(x:S,y:S)) -> NORM(x:S) REM(g(x:S,y:S),s(z:S)) -> REM(x:S,z:S) -> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: REM(g(x:S,y:S),s(z:S)) -> REM(x:S,z:S) ->->-> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil ->->Cycle: ->->-> Pairs: NORM(g(x:S,y:S)) -> NORM(x:S) ->->-> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil ->->Cycle: ->->-> Pairs: F(x:S,g(y:S,z:S)) -> F(x:S,y:S) ->->-> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil
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