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TRS Standard pair #516967676
details
property
value
status
complete
benchmark
#4.37.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.140028953552 seconds
cpu usage
0.052998924
max memory
3207168.0
stage attributes
key
value
output-size
2727
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) (RULES f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) g(c(x:S,s(y:S))) -> g(c(s(x: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(c(s(x:S),y:S)) -> F(c(x:S,s(y:S))) G(c(x:S,s(y:S))) -> G(c(s(x:S),y:S)) -> Rules: f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) Problem 1: SCC Processor: -> Pairs: F(c(s(x:S),y:S)) -> F(c(x:S,s(y:S))) G(c(x:S,s(y:S))) -> G(c(s(x:S),y:S)) -> Rules: f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: G(c(x:S,s(y:S))) -> G(c(s(x:S),y:S)) ->->-> Rules: f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) ->->Cycle: ->->-> Pairs: F(c(s(x:S),y:S)) -> F(c(x:S,s(y:S))) ->->-> Rules: f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: G(c(x:S,s(y:S))) -> G(c(s(x:S),y:S)) -> Rules: f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) -> Usable rules: Empty ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X) = 0 [g](X) = 0 [c](X1,X2) = 2.X2 [fSNonEmpty] = 0 [s](X) = 2.X + 2 [F](X) = 0 [G](X) = 2.X Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) ->Strongly Connected Components: There is no strongly connected component
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