details

property	value
status	complete
benchmark	AC49.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	0.365636 seconds
cpu usage	0.368537
user time	0.202845
system time	0.165692
max virtual memory	113188.0
max residence set size	5752.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR k l x y) (THEORY (AC plus)) (RULES app(cons(x,l),k) -> cons(x,app(l,k)) app(nil,k) -> k app(l,nil) -> l plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) sum(cons(x,nil)) -> cons(x,nil) ) Problem 1: Reduction Order Processor: -> Rules: app(cons(x,l),k) -> cons(x,app(l,k)) app(nil,k) -> k app(l,nil) -> l plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) sum(cons(x,nil)) -> cons(x,nil) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [app](X1,X2) = 2.X1 + 2.X2 + 1 [plus](X1,X2) = X1 + X2 + 2 [sum](X) = X [0] = 0 [cons](X1,X2) = X1 + X2 + 2 [nil] = 2 [s](X) = X + 2 Problem 1: Reduction Order Processor: -> Rules: app(nil,k) -> k app(l,nil) -> l plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) sum(cons(x,nil)) -> cons(x,nil) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [app](X1,X2) = X1 + 2.X2 [plus](X1,X2) = X1 + X2 + 2 [sum](X) = X [0] = 0 [cons](X1,X2) = 2.X1 + 2.X2 + 2 [nil] = 2 [s](X) = X Problem 1: Reduction Order Processor: -> Rules: app(l,nil) -> l plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) sum(cons(x,nil)) -> cons(x,nil) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [app](X1,X2) = 2.X1 + 2.X2 + 2 [plus](X1,X2) = X1 + X2 + 1 [sum](X) = X popout

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all output return to TRS Equational