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TRS Standard pair #487068344
details
property
value
status
complete
benchmark
t011.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n190.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0198299 seconds
cpu usage
0.016145
user time
0.007345
system time
0.0088
max virtual memory
0.0
max residence set size
4240.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES g(f(x:S),y:S) -> f(h(x:S,y:S)) h(x:S,y:S) -> g(x:S,f(y:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: g(f(x:S),y:S) -> f(h(x:S,y:S)) h(x:S,y:S) -> g(x:S,f(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: G(f(x:S),y:S) -> H(x:S,y:S) H(x:S,y:S) -> G(x:S,f(y:S)) -> Rules: g(f(x:S),y:S) -> f(h(x:S,y:S)) h(x:S,y:S) -> g(x:S,f(y:S)) Problem 1: SCC Processor: -> Pairs: G(f(x:S),y:S) -> H(x:S,y:S) H(x:S,y:S) -> G(x:S,f(y:S)) -> Rules: g(f(x:S),y:S) -> f(h(x:S,y:S)) h(x:S,y:S) -> g(x:S,f(y:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: G(f(x:S),y:S) -> H(x:S,y:S) H(x:S,y:S) -> G(x:S,f(y:S)) ->->-> Rules: g(f(x:S),y:S) -> f(h(x:S,y:S)) h(x:S,y:S) -> g(x:S,f(y:S)) Problem 1: Subterm Processor: -> Pairs: G(f(x:S),y:S) -> H(x:S,y:S) H(x:S,y:S) -> G(x:S,f(y:S)) -> Rules: g(f(x:S),y:S) -> f(h(x:S,y:S)) h(x:S,y:S) -> g(x:S,f(y:S)) ->Projection: pi(G) = 1 pi(H) = 1 Problem 1: SCC Processor: -> Pairs: H(x:S,y:S) -> G(x:S,f(y:S)) -> Rules: g(f(x:S),y:S) -> f(h(x:S,y:S)) h(x:S,y:S) -> g(x:S,f(y:S)) ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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