details

property	value
status	complete
benchmark	2.41.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	SK90

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0199549 seconds
cpu usage	0.020471
user time	0.008413
system time	0.012058
max virtual memory	113188.0
max residence set size	5384.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: F(x:S,g(y:S,z:S)) -> F(x:S,y:S) NORM(g(x:S,y:S)) -> NORM(x:S) REM(g(x:S,y:S),s(z:S)) -> REM(x:S,z:S) -> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil Problem 1: SCC Processor: -> Pairs: F(x:S,g(y:S,z:S)) -> F(x:S,y:S) NORM(g(x:S,y:S)) -> NORM(x:S) REM(g(x:S,y:S),s(z:S)) -> REM(x:S,z:S) -> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: REM(g(x:S,y:S),s(z:S)) -> REM(x:S,z:S) ->->-> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil ->->Cycle: ->->-> Pairs: NORM(g(x:S,y:S)) -> NORM(x:S) ->->-> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil ->->Cycle: ->->-> Pairs: F(x:S,g(y:S,z:S)) -> F(x:S,y:S) ->->-> Rules: f(x:S,g(y:S,z:S)) -> g(f(x:S,y:S),z:S) f(x:S,nil) -> g(nil,x:S) norm(g(x:S,y:S)) -> s(norm(x:S)) norm(nil) -> 0 rem(g(x:S,y:S),0) -> g(x:S,y:S) rem(g(x:S,y:S),s(z:S)) -> rem(x:S,z:S) rem(nil,y:S) -> nil The problem is decomposed in 3 subproblems. Problem 1.1: popout

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

job log

popout

actions

all output return to TRS Standard