details

property	value
status	complete
benchmark	005.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	AotoYamada_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.056169 seconds
cpu usage	0.059045
user time	0.025852
system time	0.033193
max virtual memory	113188.0
max residence set size	5552.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S f:S x:S y:S) (RULES add -> app(curry,plus) app(app(app(curry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S) app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S ) Problem 1: Innermost Equivalent Processor: -> Rules: add -> app(curry,plus) app(app(app(curry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S) app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y: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: APP(app(app(curry,f:S),x:S),y:S) -> APP(app(f:S,x:S),y:S) APP(app(app(curry,f:S),x:S),y:S) -> APP(f:S,x:S) APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) APP(app(plus,app(s,x:S)),y:S) -> APP(s,app(app(plus,x:S),y:S)) -> Rules: add -> app(curry,plus) app(app(app(curry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S) app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S Problem 1: SCC Processor: -> Pairs: APP(app(app(curry,f:S),x:S),y:S) -> APP(app(f:S,x:S),y:S) APP(app(app(curry,f:S),x:S),y:S) -> APP(f:S,x:S) APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) APP(app(plus,app(s,x:S)),y:S) -> APP(s,app(app(plus,x:S),y:S)) -> Rules: add -> app(curry,plus) app(app(app(curry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S) app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) ->->-> Rules: add -> app(curry,plus) app(app(app(curry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S) app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S ->->Cycle: ->->-> Pairs: APP(app(app(curry,f:S),x:S),y:S) -> APP(app(f:S,x:S),y:S) APP(app(app(curry,f:S),x:S),y:S) -> APP(f:S,x:S) ->->-> Rules: add -> app(curry,plus) app(app(app(curry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S) app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) -> Rules: add -> app(curry,plus) app(app(app(curry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S) app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S -> Usable rules: app(app(app(curry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S) app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [add] = 0 [app](X1,X2) = 2.X1 + X2 + 2 [0] = 0 [curry] = 0 popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Standard