Problem: F(x,y) -> c(A()) G(x) -> x h(x) -> c(x) Proof: sorted: (order) 0:F(x,y) -> c(A()) 1:G(x) -> x 2:h(x) -> c(x) ----- sorts [0>3, 0>8, 0>9, 1>7, 2>3, 3>4, 4>5, 4>6] sort attachment (non-strict) F : 8 x 9 -> 0 c : 4 -> 3 A : 5 G : 7 -> 1 h : 6 -> 2 ----- 0:F(x,y) -> c(A()) Church Rosser Transformation Processor (critical pair closing system, Thm 2.11): critical peaks: joinable Qed 1:G(x) -> x Church Rosser Transformation Processor (critical pair closing system, Thm 2.11): critical peaks: joinable Qed 2:h(x) -> c(x) Church Rosser Transformation Processor (critical pair closing system, Thm 2.11): critical peaks: joinable Qed