details

property	value
status	complete
benchmark	test830.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n186.star.cs.uiowa.edu
space	Strategy_removed_mixed_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.046257 seconds
cpu usage	0.040094
user time	0.016381
system time	0.023713
max virtual memory	113188.0
max residence set size	5472.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S X:S Y:S) (RULES f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(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(s(X:S)) -> F(X:S) G(cons(0,Y:S)) -> G(Y:S) H(cons(X:S,Y:S)) -> G(cons(X:S,Y:S)) H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S))) -> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) Problem 1: SCC Processor: -> Pairs: F(s(X:S)) -> F(X:S) G(cons(0,Y:S)) -> G(Y:S) H(cons(X:S,Y:S)) -> G(cons(X:S,Y:S)) H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S))) -> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: G(cons(0,Y:S)) -> G(Y:S) ->->-> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) ->->Cycle: ->->-> Pairs: H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S))) ->->-> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) ->->Cycle: ->->-> Pairs: F(s(X:S)) -> F(X:S) ->->-> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) The problem is decomposed in 3 subproblems. Problem 1.1: Subterm Processor: -> Pairs: G(cons(0,Y:S)) -> G(Y:S) -> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) ->Projection: pi(G) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) popout

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job log

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actions

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