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TRS Standard pair #516968101
details
property
value
status
complete
benchmark
t013.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n035.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.138617038727 seconds
cpu usage
0.070954371
max memory
4186112.0
stage attributes
key
value
output-size
5944
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 -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(0) -> 0 f(s(x:S)) -> -(s(x:S),g(f(x:S))) g(0) -> s(0) g(s(x:S)) -> -(s(x:S),f(g(x:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(0) -> 0 f(s(x:S)) -> -(s(x:S),g(f(x:S))) g(0) -> s(0) g(s(x:S)) -> -(s(x:S),f(g(x:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) F(s(x:S)) -> -#(s(x:S),g(f(x:S))) F(s(x:S)) -> F(x:S) F(s(x:S)) -> G(f(x:S)) G(s(x:S)) -> -#(s(x:S),f(g(x:S))) G(s(x:S)) -> F(g(x:S)) G(s(x:S)) -> G(x:S) -> Rules: -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(0) -> 0 f(s(x:S)) -> -(s(x:S),g(f(x:S))) g(0) -> s(0) g(s(x:S)) -> -(s(x:S),f(g(x:S))) Problem 1: SCC Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) F(s(x:S)) -> -#(s(x:S),g(f(x:S))) F(s(x:S)) -> F(x:S) F(s(x:S)) -> G(f(x:S)) G(s(x:S)) -> -#(s(x:S),f(g(x:S))) G(s(x:S)) -> F(g(x:S)) G(s(x:S)) -> G(x:S) -> Rules: -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(0) -> 0 f(s(x:S)) -> -(s(x:S),g(f(x:S))) g(0) -> s(0) g(s(x:S)) -> -(s(x:S),f(g(x:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) ->->-> Rules: -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(0) -> 0 f(s(x:S)) -> -(s(x:S),g(f(x:S))) g(0) -> s(0) g(s(x:S)) -> -(s(x:S),f(g(x:S))) ->->Cycle: ->->-> Pairs: F(s(x:S)) -> F(x:S) F(s(x:S)) -> G(f(x:S)) G(s(x:S)) -> F(g(x:S)) G(s(x:S)) -> G(x:S) ->->-> Rules: -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(0) -> 0 f(s(x:S)) -> -(s(x:S),g(f(x:S))) g(0) -> s(0) g(s(x:S)) -> -(s(x:S),f(g(x:S)))
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