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TRS Equational pair #487092840
details
property
value
status
complete
benchmark
AC29.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
Mixed_AC_and_C
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.339313 seconds
cpu usage
0.377057
user time
0.220442
system time
0.156615
max virtual memory
113188.0
max residence set size
5376.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR X Y Z x y) (THEORY (AC app) (C max')) (RULES 1 -> s(0) 2 -> s(1) 3 -> s(2) 4 -> s(3) 5 -> s(4) 6 -> s(5) 7 -> s(6) 8 -> s(7) 9 -> s(8) app(empty,X) -> X max(app(singl(x),Y)) -> max2(x,Y) max(singl(x)) -> x max'(0,x) -> x max'(s(x),s(y)) -> s(max'(x,y)) max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z) max2(x,empty) -> x max2(x,singl(y)) -> max'(x,y) ) Problem 1: Reduction Order Processor: -> Rules: 1 -> s(0) 2 -> s(1) 3 -> s(2) 4 -> s(3) 5 -> s(4) 6 -> s(5) 7 -> s(6) 8 -> s(7) 9 -> s(8) app(empty,X) -> X max(app(singl(x),Y)) -> max2(x,Y) max(singl(x)) -> x max'(0,x) -> x max'(s(x),s(y)) -> s(max'(x,y)) max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z) max2(x,empty) -> x max2(x,singl(y)) -> max'(x,y) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [1] = 2 [2] = 2 [3] = 2 [4] = 2 [5] = 2 [6] = 2 [7] = 2 [8] = 2 [9] = 2 [app](X1,X2) = X1 + X2 [max](X) = 2.X + 1 [max'](X1,X2) = X1 + X2 [max2](X1,X2) = 2.X1 + 2.X2 + 2 [0] = 1 [empty] = 0 [s](X) = X [singl](X) = X + 2 Problem 1: Reduction Order Processor: -> Rules: 2 -> s(1) 3 -> s(2) 4 -> s(3) 5 -> s(4) 6 -> s(5) 7 -> s(6) 8 -> s(7) 9 -> s(8) app(empty,X) -> X max(app(singl(x),Y)) -> max2(x,Y) max(singl(x)) -> x max'(0,x) -> x max'(s(x),s(y)) -> s(max'(x,y)) max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z) max2(x,empty) -> x max2(x,singl(y)) -> max'(x,y) ->Interpretation type: Linear ->Coefficients:
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