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TRS Standard pair #516967771
details
property
value
status
complete
benchmark
#4.32.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n087.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0230720043182 seconds
cpu usage
0.019205007
max memory
1650688.0
stage attributes
key
value
output-size
2387
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(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y: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(s(x:S),s(y:S)) -> F(x:S,s(c(s(y:S)))) F(x:S,c(y:S)) -> F(x:S,s(f(y:S,y:S))) F(x:S,c(y:S)) -> F(y:S,y:S) -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) Problem 1: SCC Processor: -> Pairs: F(s(x:S),s(y:S)) -> F(x:S,s(c(s(y:S)))) F(x:S,c(y:S)) -> F(x:S,s(f(y:S,y:S))) F(x:S,c(y:S)) -> F(y:S,y:S) -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x:S),s(y:S)) -> F(x:S,s(c(s(y:S)))) ->->-> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->->Cycle: ->->-> Pairs: F(x:S,c(y:S)) -> F(y:S,y:S) ->->-> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: F(s(x:S),s(y:S)) -> F(x:S,s(c(s(y:S)))) -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->Projection: pi(F) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: F(x:S,c(y:S)) -> F(y:S,y:S) -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->Projection: pi(F) = 2 Problem 1.2:
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