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TRS Standard pair #516964516
details
property
value
status
complete
benchmark
jones6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n007.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0761961936951 seconds
cpu usage
0.019334559
max memory
1732608.0
stage attributes
key
value
output-size
3093
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 a:S d:S k:S x:S) (RULES f(a:S,cons(x:S,k:S)) -> f(cons(x:S,a:S),k:S) f(a:S,empty) -> g(a:S,empty) g(cons(x:S,k:S),d:S) -> g(k:S,cons(x:S,d:S)) g(empty,d:S) -> d:S ) Problem 1: Innermost Equivalent Processor: -> Rules: f(a:S,cons(x:S,k:S)) -> f(cons(x:S,a:S),k:S) f(a:S,empty) -> g(a:S,empty) g(cons(x:S,k:S),d:S) -> g(k:S,cons(x:S,d:S)) g(empty,d:S) -> d: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(a:S,cons(x:S,k:S)) -> F(cons(x:S,a:S),k:S) F(a:S,empty) -> G(a:S,empty) G(cons(x:S,k:S),d:S) -> G(k:S,cons(x:S,d:S)) -> Rules: f(a:S,cons(x:S,k:S)) -> f(cons(x:S,a:S),k:S) f(a:S,empty) -> g(a:S,empty) g(cons(x:S,k:S),d:S) -> g(k:S,cons(x:S,d:S)) g(empty,d:S) -> d:S Problem 1: SCC Processor: -> Pairs: F(a:S,cons(x:S,k:S)) -> F(cons(x:S,a:S),k:S) F(a:S,empty) -> G(a:S,empty) G(cons(x:S,k:S),d:S) -> G(k:S,cons(x:S,d:S)) -> Rules: f(a:S,cons(x:S,k:S)) -> f(cons(x:S,a:S),k:S) f(a:S,empty) -> g(a:S,empty) g(cons(x:S,k:S),d:S) -> g(k:S,cons(x:S,d:S)) g(empty,d:S) -> d:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: G(cons(x:S,k:S),d:S) -> G(k:S,cons(x:S,d:S)) ->->-> Rules: f(a:S,cons(x:S,k:S)) -> f(cons(x:S,a:S),k:S) f(a:S,empty) -> g(a:S,empty) g(cons(x:S,k:S),d:S) -> g(k:S,cons(x:S,d:S)) g(empty,d:S) -> d:S ->->Cycle: ->->-> Pairs: F(a:S,cons(x:S,k:S)) -> F(cons(x:S,a:S),k:S) ->->-> Rules: f(a:S,cons(x:S,k:S)) -> f(cons(x:S,a:S),k:S) f(a:S,empty) -> g(a:S,empty) g(cons(x:S,k:S),d:S) -> g(k:S,cons(x:S,d:S)) g(empty,d:S) -> d:S The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: G(cons(x:S,k:S),d:S) -> G(k:S,cons(x:S,d:S)) -> Rules: f(a:S,cons(x:S,k:S)) -> f(cons(x:S,a:S),k:S) f(a:S,empty) -> g(a:S,empty) g(cons(x:S,k:S),d:S) -> g(k:S,cons(x:S,d:S)) g(empty,d:S) -> d:S ->Projection: pi(G) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: f(a:S,cons(x:S,k:S)) -> f(cons(x:S,a:S),k:S) f(a:S,empty) -> g(a:S,empty) g(cons(x:S,k:S),d:S) -> g(k:S,cons(x:S,d:S)) g(empty,d:S) -> d:S ->Strongly Connected Components: There is no strongly connected component
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