YES
  TPA v.1.0

Result: TRS is terminating

Default interpretations for symbols are not printed. For polynomial interpretations
and semantic labelling over N\{0,1} defaults are 2 for constants, identity for unary
symbols and x+y-2 for binary symbols. For semantic labelling over {0,1} (booleans)
defaults are 0 for constants, identity for unary symbols and disjunction for binary symbols.

[1]  TRS loaded from input file:
(1) f`1(a,f`2(b,x)) -> f`1(x,f`2(x,x))

[2]  Label this TRS using following interpretation that is a model:
[f`1(x,y)] = 0
[f`2(x,y)] = 0
[b] = 1
rest default

  thus obtaining new TRS:
(1a) f`1$00(a,f`2$11(b,x)) -> f`1$10(x,f`2$11(x,x))
(1b) f`1$00(a,f`2$10(b,x)) -> f`1$00(x,f`2$00(x,x))

[3]  Use following polynomial interpretation:
[f`2$10(x,y)] = x + y^2
[f`1$00(x,y)] = 7xy
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(1a)-(1b)

[4]  Since there are no remaining rules, termination is proved!

../qualif/toyama.trs, 0., Y
Couldn't open file <60>: 60: No such file or directory