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TRS Equational pair #487092699
details
property
value
status
complete
benchmark
AC11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.250058 seconds
cpu usage
0.186235
user time
0.097038
system time
0.089197
max virtual memory
113188.0
max residence set size
5036.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (THEORY (AC f)) (RULES f(g(f(h(a),a)),a) -> f(h(a),f(a,a)) f(g(h(a)),f(b,f(b,b))) -> f(g(f(h(a),a)),a) f(h(a),a) -> f(h(a),b) f(h(a),g(a)) -> f(g(h(a)),a) ) Problem 1: Reduction Order Processor: -> Rules: f(g(f(h(a),a)),a) -> f(h(a),f(a,a)) f(g(h(a)),f(b,f(b,b))) -> f(g(f(h(a),a)),a) f(h(a),a) -> f(h(a),b) f(h(a),g(a)) -> f(g(h(a)),a) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = X1 + X2 + 2 [a] = 2 [b] = 2 [g](X) = X + 2 [h](X) = 2.X + 2 Problem 1: Reduction Order Processor: -> Rules: f(g(h(a)),f(b,f(b,b))) -> f(g(f(h(a),a)),a) f(h(a),a) -> f(h(a),b) f(h(a),g(a)) -> f(g(h(a)),a) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = X1 + X2 + 2 [a] = 1 [b] = 1 [g](X) = X + 2 [h](X) = 2.X + 2 Problem 1: Reduction Order Processor: -> Rules: f(h(a),a) -> f(h(a),b) f(h(a),g(a)) -> f(g(h(a)),a) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = X1 + X2 + 2 [a] = 1 [b] = 0 [g](X) = 2.X + 2 [h](X) = X Problem 1: Dependency Pairs Processor: -> FAxioms: F(f(x0,x1),x2) = F(x0,f(x1,x2)) F(x0,x1) = F(x1,x0) -> Pairs: F(f(h(a),g(a)),x0) -> F(f(g(h(a)),a),x0) F(f(h(a),g(a)),x0) -> F(g(h(a)),a) F(h(a),g(a)) -> F(g(h(a)),a) -> EAxioms: f(f(x0,x1),x2) = f(x0,f(x1,x2)) f(x0,x1) = f(x1,x0) -> Rules: f(h(a),g(a)) -> f(g(h(a)),a) -> SRules: F(f(x0,x1),x2) -> F(x0,x1) F(x0,f(x1,x2)) -> F(x1,x2)
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