details

property	value
status	complete
benchmark	#4.33.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	AG01_innermost

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.070814 seconds
cpu usage	0.074315
user time	0.033723
system time	0.040592
max virtual memory	113188.0
max residence set size	5500.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S m:S n:S x:S y:S) (RULES sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) WEIGHT(cons(n:S,cons(m:S,x:S))) -> SUM(cons(n:S,cons(m:S,x:S)),cons(0,x:S)) WEIGHT(cons(n:S,cons(m:S,x:S))) -> WEIGHT(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) -> Rules: sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S Problem 1: SCC Processor: -> Pairs: SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) WEIGHT(cons(n:S,cons(m:S,x:S))) -> SUM(cons(n:S,cons(m:S,x:S)),cons(0,x:S)) WEIGHT(cons(n:S,cons(m:S,x:S))) -> WEIGHT(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) -> Rules: sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) ->->-> Rules: sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S ->->Cycle: ->->-> Pairs: WEIGHT(cons(n:S,cons(m:S,x:S))) -> WEIGHT(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) ->->-> Rules: sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) -> Rules: sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S weight(cons(n:S,cons(m:S,x:S))) -> weight(sum(cons(n:S,cons(m:S,x:S)),cons(0,x:S))) weight(cons(n:S,nil)) -> n:S -> Usable rules: Empty ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [sum](X1,X2) = 0 [weight](X) = 0 [0] = 2 [cons](X1,X2) = 2.X2 + 2 [fSNonEmpty] = 0 [nil] = 0 [s](X) = 2.X + 2 [SUM](X1,X2) = 2.X1 [WEIGHT](X) = 0 popout

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

job log

popout

actions

all output return to TRS Innermost