details

property	value
status	complete
benchmark	tpa2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.150646 seconds
cpu usage	0.134588
user time	0.073108
system time	0.06148
max virtual memory	113188.0
max residence set size	5744.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S ) Problem 1: Innermost Equivalent Processor: -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) F(s(x:S),y:S) -> -#(s(x:S),y:S) F(s(x:S),y:S) -> -#(y:S,s(x:S)) F(s(x:S),y:S) -> F(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) F(s(x:S),y:S) -> P(-(s(x:S),y:S)) F(s(x:S),y:S) -> P(-(y:S,s(x:S))) F(x:S,s(y:S)) -> -#(s(y:S),x:S) F(x:S,s(y:S)) -> -#(x:S,s(y:S)) F(x:S,s(y:S)) -> F(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) F(x:S,s(y:S)) -> P(-(s(y:S),x:S)) F(x:S,s(y:S)) -> P(-(x:S,s(y:S))) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S Problem 1: SCC Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) F(s(x:S),y:S) -> -#(s(x:S),y:S) F(s(x:S),y:S) -> -#(y:S,s(x:S)) F(s(x:S),y:S) -> F(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) F(s(x:S),y:S) -> P(-(s(x:S),y:S)) F(s(x:S),y:S) -> P(-(y:S,s(x:S))) F(x:S,s(y:S)) -> -#(s(y:S),x:S) F(x:S,s(y:S)) -> -#(x:S,s(y:S)) F(x:S,s(y:S)) -> F(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) F(x:S,s(y:S)) -> P(-(s(y:S),x:S)) F(x:S,s(y:S)) -> P(-(x:S,s(y:S))) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) ->->-> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S ->->Cycle: ->->-> Pairs: F(s(x:S),y:S) -> F(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) F(x:S,s(y:S)) -> F(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) ->->-> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S popout

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job log

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actions

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