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(x,f`2(y,z)) -> g`1(x,g`2(y,z))
(2) g`1(0,g`2(1,x)) -> f`1(x,f`2(x,x))
(3) a -> b
(4) a -> c

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

  thus obtaining new TRS:
(1a) f`1$11(x,f`2$11(y,z)) -> g`1$11(x,g`2$11(y,z))
(1b) f`1$11(x,f`2$10(y,z)) -> g`1$11(x,g`2$10(y,z))
(1c) f`1$11(x,f`2$01(y,z)) -> g`1$11(x,g`2$01(y,z))
(1d) f`1$10(x,f`2$00(y,z)) -> g`1$10(x,g`2$00(y,z))
(1e) f`1$01(x,f`2$11(y,z)) -> g`1$01(x,g`2$11(y,z))
(1f) f`1$01(x,f`2$10(y,z)) -> g`1$01(x,g`2$10(y,z))
(1g) f`1$01(x,f`2$01(y,z)) -> g`1$01(x,g`2$01(y,z))
(1h) f`1$00(x,f`2$00(y,z)) -> g`1$00(x,g`2$00(y,z))
(2a) g`1$01(0,g`2$11(1,x)) -> f`1$11(x,f`2$11(x,x))
(2b) g`1$01(0,g`2$10(1,x)) -> f`1$00(x,f`2$00(x,x))
(3a) a -> b
(4a) a -> c

[3]  Use following polynomial interpretation:
[g`1$01(x,y)] = 7xy
[f`1$01(x,y)] = 7xy
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(2a)-(2b)

[4]  Unlabel this TRS to obtain the one consisting of the rules:
(1), (3)-(4)

[5]  Use following polynomial interpretation:
[a] = 3
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(3)-(4)

[6]  Use following polynomial interpretation:
[f`1(x,y)] = x + y + 1
rest default

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

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

../tpdb/TRS/AProVE/forward_instantiation2.trs, 0.01, Y
Couldn't open file <60>: 60: No such file or directory