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	n187.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0177809 seconds
cpu usage	0.018151
user time	0.007085
system time	0.011066
max virtual memory	113188.0
max residence set size	4364.0

stage attributes

key	value
starexec-result	YES

output

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 The problem is finite. Problem 1.2: Subterm Processor: popout

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