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TRS Standard pair #487067864
details
property
value
status
complete
benchmark
2.49.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n178.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.019608 seconds
cpu usage
0.020093
user time
0.005271
system time
0.014822
max virtual memory
113188.0
max residence set size
5284.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES a(c(d(x:S))) -> c(x:S) u(b(d(d(x:S)))) -> b(x:S) v(a(a(x:S))) -> u(v(x:S)) v(a(c(x:S))) -> u(b(d(x:S))) v(c(x:S)) -> b(x:S) w(a(a(x:S))) -> u(w(x:S)) w(a(c(x:S))) -> u(b(d(x:S))) w(c(x:S)) -> b(x:S) ) Problem 1: Dependency Pairs Processor: -> Pairs: V(a(a(x:S))) -> U(v(x:S)) V(a(a(x:S))) -> V(x:S) V(a(c(x:S))) -> U(b(d(x:S))) W(a(a(x:S))) -> U(w(x:S)) W(a(a(x:S))) -> W(x:S) W(a(c(x:S))) -> U(b(d(x:S))) -> Rules: a(c(d(x:S))) -> c(x:S) u(b(d(d(x:S)))) -> b(x:S) v(a(a(x:S))) -> u(v(x:S)) v(a(c(x:S))) -> u(b(d(x:S))) v(c(x:S)) -> b(x:S) w(a(a(x:S))) -> u(w(x:S)) w(a(c(x:S))) -> u(b(d(x:S))) w(c(x:S)) -> b(x:S) Problem 1: SCC Processor: -> Pairs: V(a(a(x:S))) -> U(v(x:S)) V(a(a(x:S))) -> V(x:S) V(a(c(x:S))) -> U(b(d(x:S))) W(a(a(x:S))) -> U(w(x:S)) W(a(a(x:S))) -> W(x:S) W(a(c(x:S))) -> U(b(d(x:S))) -> Rules: a(c(d(x:S))) -> c(x:S) u(b(d(d(x:S)))) -> b(x:S) v(a(a(x:S))) -> u(v(x:S)) v(a(c(x:S))) -> u(b(d(x:S))) v(c(x:S)) -> b(x:S) w(a(a(x:S))) -> u(w(x:S)) w(a(c(x:S))) -> u(b(d(x:S))) w(c(x:S)) -> b(x:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: W(a(a(x:S))) -> W(x:S) ->->-> Rules: a(c(d(x:S))) -> c(x:S) u(b(d(d(x:S)))) -> b(x:S) v(a(a(x:S))) -> u(v(x:S)) v(a(c(x:S))) -> u(b(d(x:S))) v(c(x:S)) -> b(x:S) w(a(a(x:S))) -> u(w(x:S)) w(a(c(x:S))) -> u(b(d(x:S))) w(c(x:S)) -> b(x:S) ->->Cycle: ->->-> Pairs: V(a(a(x:S))) -> V(x:S) ->->-> Rules: a(c(d(x:S))) -> c(x:S) u(b(d(d(x:S)))) -> b(x:S) v(a(a(x:S))) -> u(v(x:S)) v(a(c(x:S))) -> u(b(d(x:S))) v(c(x:S)) -> b(x:S) w(a(a(x:S))) -> u(w(x:S)) w(a(c(x:S))) -> u(b(d(x:S))) w(c(x:S)) -> b(x:S) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: W(a(a(x:S))) -> W(x:S) -> Rules: a(c(d(x:S))) -> c(x:S) u(b(d(d(x:S)))) -> b(x:S) v(a(a(x:S))) -> u(v(x:S)) v(a(c(x:S))) -> u(b(d(x:S))) v(c(x:S)) -> b(x:S) w(a(a(x:S))) -> u(w(x:S)) w(a(c(x:S))) -> u(b(d(x:S))) w(c(x:S)) -> b(x:S) ->Projection: pi(W) = 1
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